Abstract
In this work we investigate the use of OWA operators in color image reduction. Since the RGB color scheme can be seen as a Cartesian product of lattices, we use the generalization of OWA operators to any complete lattice. However, the behavior of lattice OWA operators in image processing is not easy to predict. Therefore, we propose an orness measure that generalizes the orness measure given by Yager for usual OWA operators. With the aid of this new measure, we are able to classify each OWA operator and to analyze how its properties affect the results of applying OWA operators in an algorithm for reducing color images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Beliakov, G., Bustince, H., Paternain, D.: Image reduction using means on discrete product lattice. IEEE Trans. Image Process. 21, 1070–1083 (2012)
Beliakov, G., Bustince, H., Calvo, T.: A Practical Guide to Averaging Functions. Springer, Heidelberg (2016)
De Baets, B., Mesiar, R.: Triangular norms on product lattices. Fuzzy Sets Syst. 104, 61–75 (1999)
Dujmović, J.J.: A generalization of some functions in continuous mathematical logic - evaluation functions and its applications (In Serbo-Croatian). In: Proceedings of the Informatica Conference, Bled, paper d27, Yugoslavia (1973)
Galar, M., Fernandez, J., Beliakov, G., Busince, R.: Interval-valued fuzzy sets applied to stereo matching of color images. IEEE Trans. Image Process. 20, 1949–1961 (2011)
Grätzer, G.: General Lattice Theory. Birkhäuser Verlag, Basel (1978)
Kishor, A., Singh, A.K., Pal, N.R.: Orness measure of OWA operators: a new approach. IEEE Trans. Fuzzy Syst. 22, 1039–1045 (2014)
Komorníková, M., Mesiar, R.: Aggregation functions on bounded partially ordered sets and their classification. Fuzzy Sets Syst. 175, 48–56 (2011)
Lizasoain, I., Moreno, C.: OWA operators defined on complete lattices. Fuzzy Sets Syst. 224, 36–52 (2013)
González-Hidalgo, M., Massanet, S.: A fuzzy mathematical morphology based on discrete t-norms: fundamentals and applications to image processing. Soft Comput. 18, 2297–2311 (2014)
Paternain, D., Fernandez, J., Bustince, H., Mesiar, R., Beliakov, G.: Construction of image reduction operators using averaging aggregation functions. Fuzzy Sets Syst. 261, 87–111 (2015)
Perfilieva, I.: Fuzzy transforms: theory and applications. Fuzzy Sets Syst. 157, 993–1023 (2006)
Perfilieva, I., Kreinovich, V.: F-transform in view of aggregation functions. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds.) Aggregation Functions in Theory and in Practise. AISC, vol. 228, pp. 393–400. Springer, Heidelberg (2013)
Yager, R.R.: On ordered weighting averaging aggregation operators in multicriteria decision-making. IEEE Trans. Syst. Man Cybern. 18, 183–190 (1988)
Yager, R.R.: Families of OWA operators. Fuzzy Sets Syst. 59, 125–148 (1993)
Zhou, W., Boviz, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)
Acknowledgments
D. Paternain and H. Bustince have been partially supported by Spanish project TIN2013-40765-P. R. Mesiar has been partially supported by grant APVV-14-0013.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
Paternain, D., Ochoa, G., Lizasoain, I., Barrenechea, E., Bustince, H., Mesiar, R. (2016). On the Use of Lattice OWA Operators in Image Reduction and the Importance of the Orness Measure. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 610. Springer, Cham. https://doi.org/10.1007/978-3-319-40596-4_52
Download citation
DOI: https://doi.org/10.1007/978-3-319-40596-4_52
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40595-7
Online ISBN: 978-3-319-40596-4
eBook Packages: Computer ScienceComputer Science (R0)